Why don't you look on the demo source http://photon.komoot.de (Right click > Show source or Ctrl + u with the keyboard)?
I've done a minimum example below just to try and it works
<!doctype html>
<html lang="en">
<head>
<meta charset="utf-8">
<title>Photon, search-as-you-type with OpenStreetMap</title>
<link rel="stylesheet" href="http://cdn.leafletjs.com/leaflet-0.7.2/leaflet.css"/>
<link rel="stylesheet" href="http://photon.komoot.de/static/leaflet.photon/leaflet.photon.css">
<link rel="stylesheet" href="http://photon.komoot.de/static/css/app.css">
</head>
<body>
<div class="map" id="map"></div>
<script src="http://cdn.leafletjs.com/leaflet-0.7.2/leaflet-src.js"></script>
<script src="http://photon.komoot.de/static/leaflet.photon/leaflet.photon.js"></script>
<script src="http://photon.komoot.de/static/js/app.js"></script>
</body>
</html>
For fair use, download each file on your own server and never link directly to those remote files: it's only for the demo purpose.